M. Vidal, A. M. Aguilera del Pino
Functional principal component analysis (FPCA) has a central role in many classical functional statistical methods. However, this technique exploits the uncorrelatedness rather than other stronger properties, such as independence. High dimensional problems are progressively being adapted to the functional setting as there is a compelling need to disentangle the complexity of the data to a reduced number of variables whose linearity and smootheness is translated into highly interpretable outcomes. As an extension of the classical FPCA, we introduce a plethora of functional independent component models that go beyond the traditional methods of data reduction. The presented formulations are based on the spectral decomposition of a kurtosis operator surrogate on a sphering transformation derived from the factorization of the precision operator composed in a secondary space. We investigate optimality regarding the patterns of variability mixed in the data.
Keywords: Functional independence; Kurtosis operator; Whitening operator
Scheduled
GT06 Functional Data Analysis II. Tools and apps
June 8, 2022 4:00 PM
Grade Hall
